U.S. patent number 4,570,119 [Application Number 06/552,209] was granted by the patent office on 1986-02-11 for method for visualization of in-plane fluid flow by proton nmr imaging.
This patent grant is currently assigned to General Electric Company. Invention is credited to James R. MacFall, Felix W. Wehrli.
United States Patent |
4,570,119 |
Wehrli , et al. |
February 11, 1986 |
Method for visualization of in-plane fluid flow by proton NMR
imaging
Abstract
A method for visualizing in-plane flow utilizing an NMR pulse
sequence to produce a plurality of odd and even spin-echo signals
occurring respectively at echo delay times, T.sub.E, of 2.tau.,
6.tau., 10.tau., etc., and 4.tau., 8.tau., 12.tau., etc. In the
preferred embodiment, a fictitious spin-echo amplitude is
calculated from the odd and even spin-echo signals at an echo delay
time T.sub.E =0, for example. The calculated values for the odd
spin-echo signals are lower than those calculated for the even
spin-echo signals due to incomplete rephasing of the odd spin-echo
signals in the presence of a read-out magnetic field gradient and
flow. Subtraction of the calculated image pixel value of the odd
spin-echo signals from the calculated pixel values of the even
spin-echo signals results in a difference image which highlights
the flowing nuclear spins. The image pixels due to stationary
nuclear spins experience exact cancellation.
Inventors: |
Wehrli; Felix W. (Shorewood,
WI), MacFall; James R. (Hartland, WI) |
Assignee: |
General Electric Company
(Milwaukee, WI)
|
Family
ID: |
24204363 |
Appl.
No.: |
06/552,209 |
Filed: |
November 15, 1983 |
Current U.S.
Class: |
324/306;
324/309 |
Current CPC
Class: |
G01R
33/563 (20130101); G01P 5/001 (20130101) |
Current International
Class: |
G01P
5/00 (20060101); G01R 33/54 (20060101); G01R
33/563 (20060101); G01R 033/08 () |
Field of
Search: |
;324/300,306,307,309,311,313,314 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Tokar; Michael J.
Attorney, Agent or Firm: Gerasimow; Alexander M. Stoner;
Douglas E.
Claims
What is claimed is:
1. A method of imaging nuclear spin flow in a predetermined object
region, which region is positioned in a homogeneous magnetic field,
the flow within the region having a velocity component in the
direction of a read-out magnetic field gradient, said method
comprising:
(a) exciting to resonance a plurality of nuclear spins in the
predetermined region of said object;
(b) subjecting said excited nuclear spins to a phase-encoding
magnetic field gradient having a plurality of programmable
amplitude-duration products;
(c) causing said excited nuclear spins to produce a plurality of
even and odd numbered spin-echo signals, the odd numbered ones of
said spin-echo signals having reduced amplitudes relative to
even-numbered ones of said spin-echo signals due to flow in the
presence of the read-out magnetic field gradient;
(d) sampling said spin-echo signals in the presence of the read-out
gradient;
(e) repeating, in the course of a complete scan of said
predetermined region, steps (a)-(d) a number of times equal to the
plurality of programmable amplitude-duration products of said
phase-encoding gradient;
(f) Fourier analyzing said even and odd spin-echo signals to
generate corresponding even and odd image pixel data arrays;
(g) combining corresponding image pixel data in the even and odd
pixel arrays to eliminate image contributions due to stationary
nuclear spins, leaving substantially only signal contributions due
to flowing nuclear spins in the predetermined region; and
(h) displaying pixel data corresponding to flowing nuclear
spins.
2. The method of claim 1 wherein said step of combining comprises
the step of extrapolating the actual pixel data derived from the
odd-numbered spin-echo signals and extrapolating the actual pixel
data derived from the even-numbered spin-echo signals to a
predetermined spin-echo time T.sub.E, such that the combination of
the extrapolated pixel values results in difference pixel values
highlighting flowing nuclear spins, while stationary nuclear spin
pixel data is substantially cancelled.
3. The method of claim 2 wherein said step of combining comprises
subtracting the extrapolated image pixel data.
4. The method of claim 3 wherein said predetermined spin-echo time
is selected such that T.sub.E =0.
5. The method of claim 3 wherein said predetermined spin-echo time
is selected such that T.sub.E .noteq.0.
6. The method of claim 3 wherein said step of exciting comprises
irradiating said object with a selective RF pulse in the presence
of a magnetic field gradient so as to excite nuclear spins
substantially in the predetermined region, including any nuclear
spins flowing therein.
7. The method of claim 6 wherein said RF pulse comprises a
selective 90.degree. RF pulse.
8. The method of claim 6 wherein said phase-encoding gradient is
applied in a direction orthogonal to the direction of the read-out
gradient.
9. The method of claim 8 wherein said step (c) for producing a
plurality of spin-echo signals comprises irradiating said region
with a plurality of 180.degree. RF pulses applied in the direction
of said phase-encoding gradient.
Description
BACKGROUND OF THE INVENTION
This invention relates to methods utilizing nuclear magnetic
resonance (NMR) techniques for imaging fluid flow. The invention
has particular applicability, but is not limited, to the
measurement of blood flow in medical diagnostic studies.
By way of background, the nuclear magnetic resonance phenomenon
occurs in atomic nuclei having an odd number of protons and/or
neutrons. Due to the spin of the protons and the neutrons, each
such nucleus exhibits a magnetic moment, such that, when a sample
composed of such nuclei is paced in a static, homogeneous magnetic
field, B.sub.o, a greater number of nuclear magnetic moments align
with the field to produce a net macroscopic magnetization M in the
direction of the field. Under the influence of the magnetic field
B.sub.o, the magnetic moments precess about the axis of the field
at a frequency which is dependent on the strength of the applied
magnetic field and on the characteristics of the nuclei. The
angular precession frequency, .omega., also referred to as the
Larmor frequency, is given by the equation .omega.=.gamma.B, in
which .gamma. is the gyromagnetic ratio which is constant for each
NMR isotope and wherein B is the magnetic field acting upon the
nuclear spins. It will be thus apparent that the resonant frequency
is dependent on the strength of the magnetic field in which the
sample is positioned.
The orientation of magnetization M, normally directed along the
magnetic field B.sub.o, may be perturbed by the application of
magnetic fields oscillating at the Larmor frequency. Typically,
such magnetic fields designated B.sub.1 are applied orthogonal to
the direction of the static magnetic field by means of a
radio-frequency (RF) pulse through coils connected to a
radio-frequency transmitting apparatus. The effect of field B.sub.1
is to rotate magnetization M about the direction of the B.sub.1
field. This may be best visualized if the motion of magnetization M
due to the application of RF pulses is considered in a Cartesian
coordinate system which rotates at a frequency substantially equal
to the resonant frequency about the main magnetic field B.sub.o in
the same direction in which the magnetization M precesses. In this
case, the B.sub.o field is chosen to be directed in the positive
direction of the Z axis, which, in the rotating Cartesian system,
is designated Z' to distinguish it from the fixed-coordinate
system. Similarly, the X and Y axes are designated X' and Y'.
Bearing this in mind, the effect of an RF pulse, then, is to rotate
magnetization M, for example, from its direction along the positive
Z' axis toward the transverse plane defined by the X' and Y' axes.
An RF pulse having either sufficient magnitude or duration to
rotate magnetization M into the transverse plane (i.e., 90.degree.
from the direction of the B.sub.o field) is conveniently referred
to as a 90.degree. RF pulse. Similarly, if either the magnitude or
the duration of an RF pulse is selected to be twice that of a
90.degree. pulse, magnetization M will change direction from the
positive Z' axis to the negative Z' axis. This kind of an RF pulse
is referred to as a 180.degree. RF pulse, or for obvious reasons,
as an inverting pulse. It should be noted that a 90.degree. or a
180.degree. RF pulse will rotate magnetization M through the
corresponding number of degrees from any initial direction of
magnetization M. It should be further noted that an NMR signal will
only be observed if magnetization M has a net transverse component
(perpendicular to B.sub.o) in the transverse plane. A 90.degree. RF
pulse produces maximum net transverse magnetization in the
transverse plane since all of magnetization M is in that plane,
while a 180.degree. RF pulse does not produce any transverse
magnetization.
RF pulses may be selective or nonselective. Selective pulses are
typically modulated to have a predetermined frequency content so as
to excite nuclear spins situated in preselected regions of the
sample having precession frequencies as predicted by the Larmor
equation. The selective pulses are applied in the presence of
localizing magnetic-field gradients. Nonselective pulses generally
affect all of the nuclear spins situated within the field of the RF
pulse transmitter coil and are typically applied in the absence of
localizing magnetic field gradients.
There are two exponential time constants associated with
longitudinal and transverse magnetizations. The time constants
characterize the rate of return to equilibrium of these
magnetization components following the application of perturbing RF
pulses. The first time constant is referred to as the spin-lattice
relaxation time (T.sub.1) and is the constant for the longitudinal
magnetization to return to its equilibrium value. Spin-spin
relaxation time (T.sub.2) is the constant for the transverse
magnetization to return to its equilibrium value in a perfectly
homogeneous field B.sub.o. In fields having inhomogeneities, the
time constant for transverse magnetization is governed by a
constant denoted T.sub.2 *, with T.sub.2 * being less than T.sub.2.
In some instances, it is desirable to rapidly dissipate transverse
magnetization component by applying a magnetic field gradient, as
will be described more fully hereinafter.
There remains to be considered the use of magnetic field gradients
to encode spatial information (used to reconstruct images, for
example) into NMR signals. Typically, three such gradients are
necessary:
The G.sub.x, G.sub.y, and G.sub.z gradients are constant throughout
the imaging slice, but their magnitudes are typically time
dependent. The magnetic fields associated with the gradients are
denoted, respectively, b.sub.x, b.sub.y, and b.sub.z, wherein
within the volume.
The NMR phenomenon has been utilized by structural chemists to
study in vitro the molecular structure of organic molecules. More
recently, NMR has been developed into an imaging modality utilized
to obtain transaxial images of anatomical features of live human
subjects, for example. Such images depicting nuclear-spin
distribution (typically protons associated with water in tissue)
spin lattice (T.sub.1), and/or spin-spin (T.sub.2) relaxation
constants are of medical diagnostic value in determining the state
of health of tissue in the region examined. NMR techniques have
also been extended to in-vivo spectroscopy of such elements as
phosphorus and carbon, for example, providing researchers with the
tools for the first time to study chemical processes in a living
organism. Equally important is the use of NMR as a non-invasive
modality to study the direction and velocity of blood flows. Blood
flow studies typically rely on NMR signals produced by protons
associated with water molecules contained in blood fluid. It is
with the flow measurement application of NMR that the present
invention is concerned.
Most conventional flow imaging techniques are either based on
time-of-flight principles, phase encoding, or modulation of the
free precession frequency due to flow along a gradient during the
free precessiuon interval. These techniques are described
respectively by I. R. Young, et al, Am. J. Roentgenol. Vol. 137, p.
895 (1981); P. R. Moran, Mag. Res. Img., Vol. 1, pp. 197-203
(1982); and H. A. Lent, et al, Second Annual Meeting of The Society
of Magnetic Resonance in Medicine, San Francisco, Aug. 16-19, 1983,
Abstract page 211 in Book of Abstracts. Semi-quantitative flow
studies have also been conducted by making use of the standard
spin-echo sequence in which the signal intensity in the presence of
fluid flow is reduced due to a combination of dephasing effects
occurring during the interpulse interval (i.e., the time between
the 90.degree. excitation and the 180.degree. inverting pulses).
The semi-quantitative techniques have also taken advantage of the
dephasing effects occurring during the time between successive
repetitions of the pulse sequence. Another effect utilized in
semi-quantitative flow studies has its origin in a reduction of the
spin-echo signal amplitude due to the motion of nuclear spins in
the presence of a magnetic field gradient, as first described by
Carr and Purcell, Physics Rev., Vol. 94, p. 630 (1954). The method
for visualization of in-plane flow in accordance with the invention
makes use of the latter phenomenon in a unique and unobvious
manner.
It is one object of the invention to provide a method for
reconstructing pure-flow images in which contributions from
stationary nuclear spins are removed by cancellation.
It is another object of the invention to provide a method for
reconstructing flow images which is compatible with conventional
multiple echo proton image reconstruction techniques.
SUMMARY OF THE INVENTION
In accordance with the invention a method is provided for imaging
nuclear spin flow in a predetermined object region. The region is
positioned in a homogeneous magnetic field and is oriented relative
to a read-out magnetic field gradient such that the flow has a
velocity component in the direction thereof. The nuclear spins in
the predetermined region are excited to resonance and then
subjected to a phase-encoding gradient having a plurality of
programmable amplitude-duration products. A plurality of each of
odd- and even-numbered spin-echo signals is produced (in the
preferred embodiment) by irradiating the object region with an
equal plurality of inverting RF pulses. The odd ones of the
spin-echo signals have reduced amplitudes relative to the even ones
of the spin-echo signals due to the dephasing effects induced by
flow in the presence of the read-out gradient. The odd and even
echo signals are sampled and Fourier analyzed to yield,
respectively, odd and even image pixel data arrays. The
corresponding image pixel values in each of the arrays is then
combined to eliminate image contributions due to stationary nuclear
spins, leaving substantially only difference signal contributions
due to flowing nuclear spins in the predetermined region. The
obtained difference signals can be displayed to yield an image
emphasizing flowing nuclear spins.
BRIEF DESCRIPTION OF THE DRAWING
The features of the invention believed to be novel are set forth
with particularity in the appended claims. The invention itself,
however, both as to its organization and method of operation,
together with further objects and advantages thereof, may best be
understood by reference to the following description taken in
conjunction with the accompanying drawings in which:
FIG. 1a illustrates an NMR sample positioned in a static magnetic
field and having a planar volume defined therein by selective
excitation;
FIG. 1b is a top view of the planar volume selected in FIG. 1a and
which includes a vessel for fluid flow;
FIG. 2 depicts an exemplary embodiment of a four-spin-echo NMR
pulse sequence useful with the inventive method;
FIG. 3 illustrates a train of NMR spin-echo signals produced by
stationary nuclear spins;
FIG. 4 is similar to FIG. 3 and depicts a train of NMR spin-echo
signals having variable amplitudes due to flow of nuclear
spins;
FIG. 5 depicts the dephasing of nuclear spins in the planar volume
under the influence of a magnetic field gradient; and
FIG. 6 depicts graphically the differential phases between odd and
even spin-echo signals.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1a depicts an NMR sample 100 situated in a static homogeneous
magnetic field B.sub.o directed in the positive Z-axis direction of
the Cartesian coordinate system. The Z axis is selected to be
coincident with the longitudinal axis 106 of sample 100. The origin
of the coordinate system is tken to be the center of the sample,
which is also at the center of a planar slice 105 selected by the
principle of selective excitation in the presence of a magnetic
field gradient, as will be described hereinafter with reference to
FIG. 2. There is also shown in FIG. 1a a vessel 108 shown by way of
example as being generally parallel to the X axis. Vessel 108 acts
as a conduit for fluid flow and in medical diagostic applications
may, in fact, comprise a blood vessel. The B.sub.o field is applied
continuously during NMR studies, and therefore, is not shown on any
of the Figures depicting pulse sequences.
FIG. 2 depicts a two-dimensional spin-warp imaging sequence which
is a special case of the NMR imaging method known as Fourier
transform NMR. Referring now to FIG. 2, it will be observed that in
interval 1 indicated along the horizontal axis a positive G.sub.z
gradient pulse is applied. The direction of the G.sub.z gradient is
arbitrarily selected to be in the positive Z-axis direction of the
Cartesian coordinate system and coincides with the direction of the
B.sub.o magnetic field. Also, in interval 1, a selective 90.degree.
RF pullse is applied in the presence of the G.sub.z gradient pulse
so as to excite nuclear spins in planar volume 105 shown in FIG.
1a. The thickness in .DELTA.Z of slice 105 and its position along
axis 106 of sample 100 are determined by the amplitude of the
G.sub.z gradient and the frequency content of the selective
90.degree. RF pulse. To practice the method of the invention, the
position of slice 105 is selected so as to include therein vessel
108 which contains the fluid flow to be studied. The orientation of
vessel 108 should in general be such as to include a velocity
component in the direction of a read-out gradient which is
described hereinafter. In the configuration depicted in FIG. 1a,
vessel 108 is shown substantially parallel to the X axis. In this
case, the read-out gradient would also be applied in the X-axis
direction. In practice, the direction of the read-out gradient need
not be restricted to the X axis. In the preferred embodiments of
the invention, the RF pulse is modulated by a sinc function (sin
x/x) so as to preferentially excite nuclear spins in an imaging
slice having a substantially rectangular profile. The 90.degree. RF
pulse can also be modulated by other functions such a a Gaussian
function in which case the profile of slice 105 will be
Gaussian.
At the end of interval 1, the excited nuclear spins precess at the
same frequency but are out of phase with one another, due to the
dephasing effect of the G.sub.z gradient. Phase coherence in the
excited nuclear spins is re-established by the application in
interval 2 of a negative G.sub.z gradient pulse. Typically, the
time interval of the waveform of the G.sub.z gradient over interval
2 required to rephase the nuclear spins is selected to be
approximately equal to the negative one half of the time integral
of the G.sub.z gradient waveform in interval 1. Also, during
interval 2, a phase-encoding G.sub.y gradient is applied
simultaneously with the application of a positive G.sub.x gradient
pulse. In the preferred embodiment, G.sub.y gradient has a single,
peak amplitude during the n'th repetition of the sequence
comprising intervals 1-10 as shown in FIG. 2. In each successive
application, such as the (n+1)th repetition of the sequence, a
different amplitude of the G.sub.y gradient is selected. The
G.sub.y gradient encodes spatial information in the Y-axis
direction by introducing a twist in the orientation of the
transverse magnetization by a multiple of 2.pi.. Following the
application of a first phase-encoding gradient, the transverse
magnetization is twisted into a one-turn helix. Each different
amplitude of the G.sub.y gradient introduces a different degree of
twist (phase encoding). The number, n, of programmable G.sub.y
gradient amplitudes is chosen to be equal to the number of
resolution elements (typically 128 or 256) the reconstructed image
will have in the Y-axis direction. It will be recognized that,
although the preferred embodiment of the pulse sequence is
disclosed with reference to programmable G.sub.y gradient
amplitudes, phase encoding can also be achieved using
phase-encoding gradients having programmable amplitude-duration
products.
The effect of the G.sub.x gradient in interval 2 is to dephase the
nuclear spins by a predetermined amount such that, when a
180.degree. RF pulse is applied in interval 3 at a time .tau.
following the mean application of the 90.degree. RF pulse, a
spin-echo signal will be observed in interval 4. The time of
occurrence of the spin-echo signal, T.sub.E, is determined by the
intensity of the G.sub.x gradient applied in interval 2, the time
the 180.degree. pulse is applied, as well as the amplitude of the
G.sub.x gradient in interval 4. For example, for a spin echo to
occur at T.sub.E =2.tau. following the mean application of the
90.degree. RF pulse in interval 1, the amplitudes of the G.sub.x
gradients in intervals 2 and 4 must be selected such that the
integral of the G.sub.x gradient waveform over a time interval
q.sub.1 is equal to the time integral of the G.sub.x gradient
waveform over a time interval q.sub.2. In the pulse sequence
depicted in FIG. 2, additional 180.degree. RF pulses are applied in
intervals 5, 7, and 9 so as to produce NMR spin-echo signals in
intervals 6, 8, and 10, respectively. The amplitudes of successive
spin-echo signals are shown as decreasing exponentially (as
suggested by line 109, FIG. 2) at a rate which is proportional to
the transverse relaxation time T.sub.2. It should be noted that
gradient-reversal techniques could also be advantageously employed
with the method of the invention to produce the spin-echo
signals.
Spatial information is encoded in the direction of the X axis by
the application of read-out magnetic field gradient G.sub.x pulses
during the occurrence of the spin-echo signals in intervals 4, 6,
8, and 10. The effect of these gradient pulses is to cause the
nuclear spins to resonate at frequencies characteristic of their
locations with respect to the X axis. Each of the spin-echo signals
is sampled a number of times which is typically equal to the number
of resolution elements (128 or 256) the reconstructed image will
have in the X-axis direction. In the course of a complete scan of
slice 105, the G.sub.y gradient is sequenced through, for example,
128 programmable amplitudes, such that 128 different spin-echo
signals are observed in each of intervals 4, 6, 8, and 10. The data
associated with each set of spin-echo signals in each interval can
be used to reconstruct an image. The image pixel values are
obtained from the sampled signals in a well-known manner using a
two-dimensional Fourier transform (in the case of a two-dimensional
Fourier transform scheme).
FIG. 3 depicts a train of four spin-echo signals substantially
identical to those described with reference to FIG. 2. The spin
echoes are shown as having exponentially decaying amplitudes lying
along a line defined by I.sub.o e.sup.-T.sbsp.E.sup./T.sbsp.2. Such
a train of spin-echo signals is typically observed for a slice 105
having substantially stationary nuclear spins. In the absence of
flow, there is complete re-focussing of the nuclear spins such that
the phase-angle .phi. relative to the initial phase of the signal
is zero. The primary factor operating to reduce spin-echo signal
amplitude is due to the decay in the amplitude of the transverse
magnetization due to transverse (T.sub.2) relaxation. In the
ensuing description, the spin echoes occurring at times 2.tau.,
6.tau., 10.tau., etc., will be referred to as odd spin echoes;
while spin-echo signals occurring at time 4.tau., 8.tau., 12.tau.,
etc., will be referred to as the even spin-echo signals.
In accordance with the invention, slice 105 is carefully selected
to contain within the plane thereof the portion of vessel 108 in
which flow is to be studied. As indicated previously, the direction
of the vessel is selected so as to generally coincide with the
direction of the read-out gradient. The X axis has been selected by
way of example as being the direction in which the G.sub.x read-out
gradient is applied as described hereinbefore with reference to
FIG. 2. It should be noted that the read-out gradient could also be
applied in a different direction, in which case the programmable
phase amplitude gradient (G.sub.y) would be applied in a direction
orthogonal to the read-out gradient. In practice, vessel 108 need
not be oriented parallel to the direction of the read-out gradient.
All that is necessary is that a finite flow velocity component in
the direction of the read-out gradient be present.
The method of the invention will now be described with initial
reference to FIG. 1b which depicts an assembly of nuclear spins 110
flowing with a velocity v(x) in the X-axis direction in vessel 108.
Slice 105 is subjected to the NMR pulse sequence depicted in FIG. 2
in which the direction of the G.sub.x read-out gradient is
coincident with a velocity component of current flow within the
vessel. As before, 180.degree. RF pulses are applied in the
direction of the Y axis orthogonal to the direction of the B.sub.o
field so as to produce spin-echo signals at times 2.tau., 4.tau.,
6.tau., and 8.tau.. The resulting spin-echo train is illustrated in
FIG. 4 in which it will be observed that the odd spin-echo signals
occurring at times 2.tau. and 6.tau. have a diminished amplitude
relative to the same spin echoes in FIG. 3. The odd spin-echo
signals depicted in FIG. 4 decay along an exponential curve 116
defined by I.sub.o.sup.' e.sup.-T.sbsp.E.sup./T.sbsp.2. However,
their amplitudes are much reduced, due to fluid flow in the
presence of the G.sub.x gradient. Since flow in vessel 108 is
characterized by a velocity distribution given by the nature of the
flow, a dephasing of the nuclear spins occurs at a time where the
odd-numbered spin echoes are expected. The dephasing of the nuclear
spins leads to a reduction in the spin-echo signal amplitude. The
dephasing effect is illustrated graphically in FIG. 5 in which
nuclear spin isochromats schematically denoted by arrows 112 have
accumulated different phase angles .phi..sub.1, .phi..sub.2,
.phi..sub.3, and .phi..sub.4, caused by the different flow
velocities in the presence of the G.sub.x gradient.
The phase accumulation for the odd spin-echo signals will now be
described with reference to FIG. 6 which depicts the 90.degree. and
180.degree. RF pulses and the read-out G.sub.x gradient which is
active between the RF pulses in a fashion similar to that already
described with reference to FIG. 2. The incremental frequency of
the spins after traversing a distance dx in vessel 108 in the
direction of the gradient G.sub.x is d.omega.. Assuming a steady
flow within vessel 108 with a velocity v, d.omega. can then be
written
The accumulated phase angle .phi. at a time t=.tau. in which the
first 180.degree. RF pulse is applied can be expressed as ##EQU1##
The 180.degree. pulse applied at time .tau. inverts the sign of the
phase angle such that the accumulated phase angles during period
t=2.tau. can be expressed as ##EQU2## Similarly, the accumulated
phase angle during intervals t=3.tau. and t=4.tau. can be expressed
as ##EQU3## It will be noted from Equation (5) and FIG. 6 that at
t=4.tau., that is, the time of occurrence of the first even
spin-echo signal, the accumulated phase angle is equal to zero.
This is in agreement with the observed spin-echo signals and
described with reference to FIGS. 3 and 4 in which the even spin
echoes have been attenuated by T.sub.2 decay only, unaffected by
fluid flow. The increase in accumulated phase in the presence of
the G.sub.x gradient with increasing time is evident in FIG. 6 in
which the amplitude of angle .phi. is observed to be
increasing.
In accordance with the present invention, a pure flow image is
generated by adding and subtracting suitably intensity-weighted
images reconstructed from odd and even spin-echo signals. A flow
enhanced image could be obtained by summing image pixel data
derived from even spin-echo signals and subtracting image pixel
data obtained from odd spin echoes. However, exact cancellation of
the stationary proton signals cannot be achieved in this manner
because subsequent odd and even spin-echo signals do not have equal
amplitudes as is evident from FIG. 4.
It is initially beneficial to consider intensity-weighted images
obtained utilizing spin-echo-signal data from stationary protons.
For the stationary protons the image pixel values obtained from the
four successive spin-echo signals (both odd and even) are
determined by a decaying exponential (FIG. 3). In this case, the
spin-echo signals map out the T.sub.2 decay curve:
where T.sub.E represents the echo delay time, that is, the time
between the initial 90.degree. pulse and the appearance of the
echo, and where I.sub.o denotes spin-echo amplitude at zero delay
time (i.e., T.sub.E =0). From the even spin-echo signals (T.sub.E
=4.tau., 8.tau., etc.), it is possible to compute, using
curve-fitting techniques known to those skilled in the art, a
fictitious image pixel value which would be observed at, for
example, T.sub.E =0. Likewise, the same fictitious echo amplitude
is obtained from the odd echoes at T.sub.E =2.tau., 6.tau., etc.,
since their amplitudes lie at the same decay curve designated 120
in FIG. 3. Hence, by subtracting the pixel value of the odd echoes
from that of the even echoes exact signal cancellation occurs. In
the example described herein, the fictitious pixel values were
computed for T.sub.E =0. However, fictitious pixel values could
also be calculated for echo delay times T.sub.E .noteq.0, as long
as the values derived from odd and even echoes are calculated for
the same value of T.sub.E.
By contrast, if flow is present, complete refocussing occurs only
for the even echoes appearing at T.sub.E =4.tau. and 8.tau., as
shown in FIG. 4. Therefore, the computed (fictitious) spin-echo
amplitudes at time T.sub.E =0 will be different for the even and
odd spin echoes. In fact, there is only partial refocussing of the
NMR signal at T.sub.E =2.tau., 6.tau., etc. Therefore, when the
fictitious echo amplitude that would be observed at T.sub.E =0 is
calculated from the odd echoes, a much lower value I.sub.o '
calculated using the decay curve designated by reference numeral
116 is obtained, than the value I.sub.o calculated using the even
spin-echo amplitudes which decay along a curve designated 118.
Thus, contrary to the behavior for the stationary protons, the
difference between values I.sub.o ' and I.sub.o of the extrapolated
T.sub.2 decay curve for odd and even spin echoes in the case of
flowing protons will be different. Hence, the resulting difference
image derived in the manner described hereinabove will highlight
the flowing nuclear spins only, whereas those due to stationary
nuclear spins, that is, non-moving spins, will experience exact
cancellation. Images have been obtained in accordance with the
invention utilizing a spin-echo train in which the echoes occurred
at times T.sub.E =25, 50, 75, and 100 milliseconds. Although the
invention has been described with reference to a spin-echo train
comprised of four signals, the invention may be practiced with a
greater number of spin-echo signals.
From the foregoing, it will be appreciated that in accordance with
the invention, a method is provided for reconstructing pure flow
images in which contributions from stationary nuclear spins are
removed by cancellation. The method for reconstructing the flow
images is compatible with conventional multiple echo proton image
reconstruction techniques.
While this invention has been described with reference to
particular embodiments and examples, other modifications and
variations will occur to those skilled in the art in view of the
above teachings. Accordingly, it should be understood that within
the scope of the appended claims the invention may be practiced
otherwise than is specifically described.
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